D.K. Ramesh Kumar and C. V. Jayanna Solutions for Chapter: Matrices and Determinants, Exercise 1: Exercise 1

If $A+B=\left[\begin{array}{ll}1& 0\\ 1& 1\end{array}\right]$ and $A-2B=\left[\begin{array}{cc}-1& 1\\ 0& -1\end{array}\right]$ then $A=$

If $A=\left[\begin{array}{cc}-3& 4\\ 2& -1\end{array}\right]$ then the characteristic roots of $A$ are

For a real number $\propto$, let $A\left(\propto \right)$ denote the matrix, then for real numbers ${\propto }_1$ and ${\propto }_2$, $A\left({\propto }_1\right)A\left({\propto }_2\right)$

The inverse of the matrix $\left|\begin{array}{cc}5& -2\\ 3& 1\end{array}\right|$ is

If $A=\left[\begin{array}{ccc}2& 1& 5\\ 0& 3& 7\end{array}\right]$ then

The matrix $A=\left(\begin{array}{ccc}3& -1& 2\\ 1& 2& -3\\ 4& 0& -5\end{array}\right)$ is

If $A=\left(\begin{array}{ccc}2& -1& 1\\ 0& 1& 2\\ 1& 0& 1\end{array}\right)$ then

If $\left|\begin{array}{ccc}2& 1& 3\\ 8& 4& x\\ -7& 5& 1\end{array}\right|=0$ then $x$ is equal to